The present invention relates in general terms to the field of position controls of articulated systems, whose inertia varies as a function of the state of the system. This is the case with articulated manipulators, equipped with random rotary motive members (electrical, hydraulic or pneumatic) or certain machine tools. In equipment of this type, the inertia restored to the shaft of the control motor is obviously dependent on the geometrical state of the articulated system, as well as on the mass loads which the latter has to carry. The invention deals more specifically with the problem of making the real rotation angle .theta..sub.r (t) of the shaft of the control motor of the apparatus dependent on a reference value .theta..sub.c (t).
Such control systems have generally been hitherto realised with the aid of an analog structure emitting a control signal of the proportional and derived type, i.e. formed by two terms, whereof one is proportional to the error signal and the other to its derivative. Such a known control structure is shown in FIG. 1 illustrating how it is possible to constitute the error signal .epsilon.=.theta..sub.c (t)-.theta..sub.r (t) with the aid of an adder 1, which receives on the one hand the angular reference signal .theta..sub.c (t) and on the other the signal .theta..sub.r (t) corresponding to the real value of the rotation angle of a motor. This signal is introduced into a corrector 2 supplying at the output an analog signal of form G.epsilon.+.beta..epsilon.' in which G and .beta. are the gain and damping of corrector 2 and chosen in an experimental manner, as will be explained hereinafter.
The analog signal G.epsilon.+.beta..epsilon.' is then introduced into the power amplifier 3, which applies a torque .GAMMA. to motor 4. An analog transducer takes the instantaneous value of .theta..sub.r (t) on the shaft of motor 4 and supplies it be feedback loop 6 to the negative input of adder 1.
The basic equation of the dynamics applied to the shaft of motor 4 makes it possible to write the following equation (1): EQU J(d.sup.2 .theta..sub.r /dt.sup.2)+.beta..epsilon.'+G.epsilon.=0(1)
in which .epsilon.' is the derivative d.epsilon./dt relative to the time of the error signal .epsilon.. Theory and experience show that the performances, i.e. the behaviour modes of such a system (aperiodic, critical, damped oscillation) are dependent on the value respectively &lt;0, zero or &gt;0 of the discrimination .DELTA. of the preceding equation, which is .DELTA.=.beta..sup.2 -4JG.
It is clear that a dependent control structure according to FIG. 1 causes virtually insoluble problems when the inertia restored to the shaft of motor 4 is itself variable as a function of the configuration of the articulated system because, in this case, the discriminant .DELTA. also varies as a function of the same configuration and the performances of the control system are not constant. In other words, the variation of the inertia J due to the variations of the configuration of the articulated system and the loads taken up and transported leads to a mismatching of the gain G and damping .beta., whose values have been experimentally chosen for a given value J.sub.0 of the inertia J restored to the shaft of motor 4. In operation, this leads to intolerable variations compared with the reference trajectories prescribed for the controlled apparatus. In addition, a regulation system such as that of FIG. 1 is far from easy to use in robotics due to the acceleration effects for which no correction is provided, because the control system of FIG. 1 is an approximation of the first order, which completely ignores acceleration effects. These deficiencies are particularly disturbing when the articulated system to be controlled is, for example, a robot having articulated arms with a plurality of motors actuating successive joints, whose position errors can consequently be dangerously summated.
In order to solve this problem and compensate the variations of the inertia by modifications to the gain and damping during operation, the invention proposes to realise a driving torque of form: EQU .GAMMA..sub..mu. =J(G.epsilon.+.beta..epsilon.') (2)
which would lead to a closed loop equation of form: EQU (d.sup.2 .theta..sub.r /dt.sup.2)+.beta..epsilon.'+G.epsilon.=0(3)
in which the inertial variable J has disappeared.
A control system of this type, which would make it possible to also correct acceleration effects by adding a term linked with the second derivative of the position reference signal could obviously be produced on a digital computer which, on the basis of the angular position of the axis of the motor plotted by a digital coder mounted on the motor shaft, would calculate the magnitude of the torque in accordance with the above equation (2) and would supply it to a digital--analog converter. The corresponding analog signal could then be used as the input for power amplifiers, which would transform it into a signal able to actuate the motor by accurately applying torque .GAMMA..sub..mu. thereto. In practice, this theroretically possible solution is confronted by a large number of serious disadvantages, which make it virtually unusable for the following reasons:
1. All robotics equipment at present in use is designed to operate on an analog control basis and it would be necessary to completely replace existing cabling and potentiometers in order to adapt the equipment to digital operation. Moreover, it is well known that digital controls have an often disturbing sensitivity level with respect to external interference of different types. PA0 2. In the case of an incident on the computer leading to its stoppage, there would be a "freeze" of the control instructions and the current supplied to the control of the motor shaft would be maintained at their value at the time of the incident, which could lead to catastrophic movements for the manipulators and the area around them, because the movements taking place at the time of the incident could, at least in theory, continue in an unlimited manner. PA0 3. The construction of such control systems would make it necessary to use multiprocessing methods and would therefore be complex to realise. PA0 4. The speed of existing digital computers is not generally adequate to ensure under satisfactory conditions the control of a robot having a certain number of joints in series (at least 25 ms would be necessary for the calculation of the inertia coefficients and the processing of the control .GAMMA..sub..mu. in the case of a device having 6.degree. of freedom, whereas correct operation would require all the instructions to be performed in less than 3 or 4 ms). PA0 5. Digital coders are generally of a very large size and also sensitive to ionizing radiation, which can be very prejudicial when the remote manipulator or robot used is operating in an enclosure exposed to such radiation.
For all these reasons, a digital control system calculating at each instant, in accordance with the law defined in (2), the magnitude of the driving torque to be realised for accurately compensating the variations of the inertia acting on the gain and damping coefficients cannot be realised in practice.